Solve 2sqrt{3}(3sqrt{8}-sqrt{18}

$$2 \sqrt{ 3 } (3 \sqrt{ 8 } - \sqrt{ 18 }$$

Evaluate

$$6\sqrt{6}\approx 14.696938457$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{3}\left(3\times 2\sqrt{2}-\sqrt{18}\right)$$

Multiply 3 and 2 to get 6.

$$2\sqrt{3}\left(6\sqrt{2}-\sqrt{18}\right)$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$2\sqrt{3}\left(6\sqrt{2}-3\sqrt{2}\right)$$

Combine 6\sqrt{2} and -3\sqrt{2} to get 3\sqrt{2}.

$$2\sqrt{3}\times 3\sqrt{2}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{3}\sqrt{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$6\sqrt{6}$$